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Your investment portfolio consists of \$15,000 invested in only one stock-Microsoft. Suppose the risk-free rate is 5%, Microsoft stock has an expected return of 12% and a volatility of 40%, and the market portfolio has an expected return of 10% and a volatility of 18%.Under the CAPM assumptions,a. What alternative investment has the lowest possible volatility while having the same expected return as Microsoft?b. What investment has the highest possible expected return while having the same volatility as Microsoft?
Solution: Part a As per CAPM theory and its assumptions, the market portfolio is efficient. A leveraged position in the market has the highest expected return of any portfolio for a given volatility and the lowest volatility for a given expected return. Thus, lowest volatility with return same as Microsoft can be achieved by holding a leveraged position in the market portfolio Wm and (1-Wm) in risk-free rate. Expected return on portfolio = Wm * expected return on market portfolio + (1-Wm) * risk-free rate Or, 12% = Wm*10% + (1-Wm) * 5% Or, Wm = 1.4 or 140% holding in market portfolio and borrowing at 40% at risk-free rate This means investment in market portfolio at \$15,000 *1.4 = \$21,000 and borrowing at risk-free rate = \$6,000 Volatility of this portfolio = 1.4 * volatility of market portfolio = 1.4 * 0.18 = 0.252 = 25.2% Part b As per CAPM…

y and its assumptions, the market portfolio is efficient. A leveraged position in the market has the highest expected return of any portfolio for a given volatility. Thus, highest possible return can be achieved by maintaining volatility same as Microsoft by holding a leveraged position in the market portfolio Wm and (1-Wm) in risk-free rate. 0.40 = Wm * volatility of market Or, Wm = 0.40 / 0.18 = 2.22 Thus, investing 2.22 times in market portfolio or \$33,333.33 and borrowing at risk-free rate (1- Wm) or 1.22 times or \$18,500.33 achieving same volatility as Microsoft.

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